{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# PDE-FIND for Burger's Equation\n",
    "\n",
    "Samuel Rudy, 2016\n",
    "\n",
    "This notebook demonstrates PDE-FIND on Burger's equation with an added diffusive term.\n",
    "$$\n",
    "u_t + uu_x = u_{xx}\n",
    "$$\n",
    "The solution given is a single travelling wave, starting out as a Gaussian."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
    }
   ],
   "source": [
    "%pylab inline\n",
    "pylab.rcParams['figure.figsize'] = (12, 8)\n",
    "import numpy as np\n",
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "from PDE_FIND import *\n",
    "import scipy.io as sio\n",
    "import itertools"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "data = sio.loadmat('./canonicalPDEs/burgers.mat')\n",
    "u = real(data['usol'])\n",
    "x = real(data['x'][0])\n",
    "t = real(data['t'][:,0])\n",
    "dt = t[1]-t[0]\n",
    "dx = x[2]-x[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x7fe3f5afcd50>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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ClkgkUCgUPNNm9gJZ0wAURYFpmiiXy32XVKJ7zOXC3GkUyS8S64ZuSjpD9u1G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\nAHGGpW4Xr29F1CW2OiWooL84uKqf7RPzVrXxcZhvv+1dJqB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IQc3GZ/B4IaFxN4AnaO15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\nHydnXcavhBjbAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fe3f5b52090>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "X, T = np.meshgrid(x, t)\n",
    "fig1 = figure()\n",
    "ax = fig1.gca(projection='3d')\n",
    "surf = ax.plot_surface(X, T, u.T, rstride=1, cstride=1, cmap=cm.coolwarm,\n",
    "    linewidth=0, antialiased=False)\n",
    "title('Burgers Equation', fontsize = 20)\n",
    "xlabel('x', fontsize = 16)\n",
    "ylabel('t', fontsize = 16)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Construct $\\Theta (U)$ and compute $U_t$\n",
    "\n",
    "The function build_linear_system does this for us.  We specify <br>\n",
    "D = highest derivative to appear in $\\Theta$  <br>\n",
    "P = highest degree polynomial of $u$ to appear in $\\Theta$ (not including multiplication by a derivative.  <br>\n",
    "time_diff and space_diff taken via finite differences\n",
    "\n",
    "Printed out is a list of candidate functions for the PDE.  Each is a column of $\\Theta (U)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['1',\n",
       " 'u',\n",
       " 'u^2',\n",
       " 'u^3',\n",
       " 'u_{x}',\n",
       " 'uu_{x}',\n",
       " 'u^2u_{x}',\n",
       " 'u^3u_{x}',\n",
       " 'u_{xx}',\n",
       " 'uu_{xx}',\n",
       " 'u^2u_{xx}',\n",
       " 'u^3u_{xx}',\n",
       " 'u_{xxx}',\n",
       " 'uu_{xxx}',\n",
       " 'u^2u_{xxx}',\n",
       " 'u^3u_{xxx}']"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Ut, R, rhs_des = build_linear_system(u, dt, dx, D=3, P=3, time_diff = 'FD', space_diff = 'FD')\n",
    "['1'] + rhs_des[1:]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Solve for $\\xi$\n",
    "\n",
    "TrainSTRidge splits the data up into 80% for training and 20% for validation.  It searches over various tolerances in the STRidge algorithm and finds the one with the best performance on the validation set, including an $\\ell^0$ penalty for $\\xi$ in the loss function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "PDE derived using STRidge\n",
      "u_t = (-1.000987 +0.000000i)uu_{x}\n",
      "    + (0.100220 +0.000000i)u_{xx}\n",
      "   \n"
     ]
    }
   ],
   "source": [
    "# Solve with STRidge\n",
    "w = TrainSTRidge(R,Ut,10**-5,1)\n",
    "print \"PDE derived using STRidge\"\n",
    "print_pde(w, rhs_des)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Error using PDE-FIND to identify Burger's equation:\n",
      "\n",
      "Mean parameter error: 0.15935 %\n",
      "Standard deviation of parameter error: 0.06065 %\n"
     ]
    }
   ],
   "source": [
    "err = abs(np.array([(1 -  1.000987)*100, (.1 - 0.100220)*100/0.1]))\n",
    "print \"Error using PDE-FIND to identify Burger's equation:\\n\"\n",
    "print \"Mean parameter error:\", mean(err), '%'\n",
    "print \"Standard deviation of parameter error:\", std(err), '%'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Now identify the same dynamics but with added noise.\n",
    "\n",
    "The only difference from above is that finite differences work poorly for noisy data so here we use polynomial interpolation.  With deg_x or deg_t and width_x or width_t we specify the degree number of points used to fit the polynomials used for differentiating x or t.  Unfortunately, the result can be sensitive to these."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "numpy.random.seed(0)\n",
    "un = u + 0.01*std(u)*np.random.randn(u.shape[0],u.shape[1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "Utn, Rn, rhs_des = build_linear_system(un, dt, dx, D=3, P=3, time_diff = 'poly',\n",
    "                                       deg_x = 4, deg_t = 4, \n",
    "                                       width_x = 10, width_t = 10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "PDE derived using STRidge\n",
      "u_t = (-1.009655 +0.000000i)uu_{x}\n",
      "    + (0.102966 +0.000000i)u_{xx}\n",
      "   \n"
     ]
    }
   ],
   "source": [
    "# Solve with STRidge\n",
    "w = TrainSTRidge(Rn,Utn,10**-5,1)\n",
    "print \"PDE derived using STRidge\"\n",
    "print_pde(w, rhs_des)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Error using PDE-FIND to identify Burger's equation with added noise:\n",
      "\n",
      "Mean parameter error: 1.96575 %\n",
      "Standard deviation of parameter error: 1.00025 %\n"
     ]
    }
   ],
   "source": [
    "err = abs(np.array([(1 -  1.009655)*100, (.1 - 0.102966)*100/0.1]))\n",
    "print \"Error using PDE-FIND to identify Burger's equation with added noise:\\n\"\n",
    "print \"Mean parameter error:\", mean(err), '%'\n",
    "print \"Standard deviation of parameter error:\", std(err), '%'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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